Problem 9 IYPT 2027: 9. Photographic bokeh

Problem Description & Analysis

Bokeh is an effect observed in photographs that show objects at different distances from the camera and have both sharp and out-of-focus areas. If a slit is placed in front of the lens of the camera, the image may have unusual anisotropic distortions in out-of-focus areas, while in-focus areas remain undistorted and sharp. Investigate how the properties and sharpness of resulting images depend on relevant parameters.

Related Images

Interactive Simulation (Python)

This simulation runs directly in your browser — no Python installation needed. Initial loading may take a few seconds.

فاصلهٔ کانونی f (mm) 50 mm

عدد دیافراگم N (f/N) 2.8

فاصلهٔ فوکوس s (m) 2 m

فاصلهٔ سوژه (m) 5 m

Press the button below to start.

Python Code Lab

Edit this starter code, enter your own experimental data, and run it directly in the browser — no Python installation required.

Python — Editable

# آزمایش بوکه — قطر دیسک بوکه برحسب عدد دیافراگم و فاصلهٔ سوژه
import numpy as np
import matplotlib.pyplot as plt

# --- بخش ۱: داده‌های شما ---
f      = 50e-3    # فاصلهٔ کانونی (m)
s      = 2.0      # فاصلهٔ فوکوس (m)
s_obj  = 5.0      # فاصلهٔ نقطهٔ نوری آزمایش (m)
# قطر دیسک بوکه اندازه‌گیری‌شده روی حسگر (mm) در f-numbers مختلف
N_meas = np.array([1.8, 2.8, 4.0, 5.6, 8.0, 11.0])
d_meas = np.array([0.61, 0.39, 0.28, 0.20, 0.14, 0.10])

# --- بخش ۲: نظریه ---
def CoC(N, s, s_obj, f):
    D = f/N
    return D * f * abs(s - s_obj) / (s_obj * (s - f))

d_th = np.array([CoC(N, s, s_obj, f)*1000 for N in N_meas])

# --- بخش ۳: نمودار ---
fig, ax = plt.subplots(figsize=(8, 4.6))
N_smooth = np.linspace(1.4, 16, 200)
d_smooth = np.array([CoC(N, s, s_obj, f)*1000 for N in N_smooth])
ax.plot(N_smooth, d_smooth, 'b-', lw=2, label='theory')
ax.plot(N_meas, d_meas, 'ro', ms=9, label='measured')
ax.set_xlabel('aperture (f-number)'); ax.set_ylabel('bokeh disc diameter (mm)')
ax.set_title('Bokeh disc vs aperture')
ax.set_xscale('log'); ax.set_yscale('log')
ax.legend(); ax.grid(True, which='both', alpha=0.3)
plt.tight_layout()

# --- بخش ۴: نتایج ---
print(" f/N   d_th(mm)  d_meas(mm)  ratio")
for N, dt, dm in zip(N_meas, d_th, d_meas):
    print(f" f/{N:4.1f}  {dt:.3f}     {dm:.3f}     {dm/dt:.2f}")
# فیت: d ∝ 1/N باید مشاهده شود
slope = np.polyfit(np.log(N_meas), np.log(d_meas), 1)[0]
print(f"nMeasured slope in log-log (should be −1): {slope:.2f}")

Ready to run

Output

Problem Description & Analysis

Related Images

Interactive Simulation (Python)

Python Code Lab

Suggested Resources